Corollary 1

Tag 02T9, permanent. Cite it as [Bourbaki, Tag 02T9].

Théories spectrales, chapter III, § 4. Perturbations dans les espaces de Banach

The functions defined by $u\mapsto$ dim Ker( $u$ ) and by $u\mapsto$ dim Coker( $u$ ) on $\mathscr{Q}\mathscr{E}(E; F)$ are upper semi-continuous. The function $u\mapsto$ ind( $u$ ) is locally constant on $\mathscr{Q}\mathscr{E}(E; F)$ .

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Nothing.